You are right about context and intonation playing a very important role in these sentences.
If you ask a taxi driver to hurry because you are in hurry by saying "Will you hurry?" you are actually asking the driver's willingness and will hurt his/her feeling.
If you are stuck in traffic, asking the driver if he will hurry may indeed hurt their feelings, since it seems obvious that their willingness to hurry is not questioned by the fact that they are simply unable to hurry. (Albeit that some drivers have very original ways to enable them to hurry even in very busy traffic, and that their willingness to do so may increase after the promise of an extra financial reward...)
Indeed, the use of "will" normally inquires directly about a person's willingness to perform a task, and we normally assume that the person is able to do so. Asking them if they are willing when they are obviously unable might be insulting. On the other hand, you could use "would" for a hypothetical situation: "If you knew Spanish, would you help me with my homework?"
"Could you ~?" is usually more polite than "Can you ~?" but only when you ask for help "Can you help me?" is more considerate than "Could you help me?" because when the answer is no the person feels more easier to say no.
"Could" is indeed usually more polite indeed. Where "can" simply asks whether the person is capable of doing something (and implying that you would appreciate they did it!), when you use "could", you are implying that they have to also have a willingness to do it.
So indeed "could you provide an example?" is more polite than "can you provide an example?", but can is the correct form to use when you are genuinely wondering if the person is able to do something:
Can you come to the dinner party this evening? => Are you able to make it, or have you another appointment?
Could you come to the dinner party this evening? => It would be much appreciated if you would come.
"Would you mind ~?" is not polite way of asking but it's rather cynical.
It is actually a very polite way of asking. "Would you mind giving me a hand?" is more polite than any of the previous forms.
However, exactly because is is so polite, it is often too polite in most circumstances! And because of that, it can be very effectively used in a cynical way, in the same way we can use formal forms of address or other (extremely) formal language.
As such, nobody will think of cynicism if a lady asks a stranger:
Would you mind helping me cross the street?
But if I address a friend of mine in this way:
Miss Jones, my dearest, smartest friend, would you mind terribly if I were to decline your kind invitation to your extremely interesting lecture on the history of quilting in 1970's rural Northumbria?
I am quite sure she, and anyone who heard it, would understand that I might be a bit cynical about the interest in the subject as well as my actual appreciation of the invitation - and most importantly, it would be understood I am not actually inquiring whether she would mind my rejection, I am assuming my rejecting should come as no surprise to her!
Compare the following sentences:
Present time
- It's very dangerous in Metropolis right now. You can be beaten up for just looking at someone the wrong way.
- It's very dangerous in Metropolis right now. You could be beaten up for just looking at someone the wrong way.
Sentence (1) presents being beaten up as a live possibility, as something that does actually happen to people. Notice that we can analyse for just looking at someone the wrong way, as some kind of condition:
1'. You can be beaten up if you just look at someone the wrong way.
Sentence (2) presents being beaten up as a hypothetical outcome of the wrong look. It is not being presented in the same way as in (1). It doesn't necessarily say that people are being beaten up for looking at people the wrong way - although we might assume that they are.
Could in sentence (2), as already mentioned, represents this outcome as a hypothetical possibility, as opposed to a live one. We could rephrase it as the following hypothetical conditional:
2'. You could be beaten up if you just look(ed) at someone the wrong way.
Remember both of these sentences refer to the present or future time. The way that we interpret you here is quite likely to affect our interpretation of the sentence. It's also quite likely to affect our choice of can or could. If you means a person in general, we are more likely to use can. If you is being used to make the listener imagine themselves in that situation, then we are more likely to use the hypothetical could.
Past time
Let's move forward twenty years. Now if we wish to make the same kind of statement but about Metropolis twenty years ago instead of now, we need to shift the tenses back to indicate past time. Example (1) would now be as in (3):
- It was very dangerous in Metropolis in those days. You could be beaten up
for just looking at someone the wrong way.
Here we see could appearing as the past form of can. This past form of can still implies that people actually were being beaten up for looking at people the wrong way. It is being presented as a live possibility for people at the time. It has exactly the same meaning as can, but refers to a past time. It does not represent hypotheticality.
However, in sentence (2) we already have past tense could, where the past tense indicates hypotheticality. If we wish to keep this hypothetical flavour, but also indicate past time, then we need to shift the tense back further. We need to use a past perfect form as in (4):
- It was very dangerous in Metropolis in those days. You could have been beaten up
for just looking at someone the wrong way.
Sentences (3) and (4) could be construed as the conditionals:
3'. You could be beaten up if you just looked at someone the wrong way.
4'. You could have been beaten up if you ('d) just looked at someone the wrong way.
So if we see a past perfect form could have this most likely represents past time reference plus hypotheticality.
Hope this helps!
Best Answer
The meaning is a slightly different nuance than you are getting from the definition and advice. The applicable meanings are: to express custom or habitual action (ex: we would meet often for lunch) or to express consent or choice (ex: would put it off if he could). See Webster.
You example doesn't quite fit because of the meaning of the verb you picked. You could say:
That could mean either that you customarily visited, or chose to visit (we wouldn't visit Chicago because we hated that city, but we would visit New York).
The reason it doesn't work with "live in" is because living somewhere is typically a long term thing; you move there and stay awhile. So it isn't a recurring activity that can be a habit. custom, or choice, when you talk about the past. There may have been an initial choice to live there, but that happened once, it isn't a recurring choice.
That said, you could contrive a situation where it might fit. Say an old timer was recounting his life. He had some kind of job that would put him in a location for a short time and then he had to move. He liked New York and over his lifetime, he chose to go back to New York to live many times. He might say "I would live in New York when I had a yearning for the big city."
Your example "...when I was young" would kind of rule out even that contrived scenario because there wouldn't ordinarily be enough time when you were young to make living in one place among others a frequent occurrence.